Sample Size Determination: How Many Respondents Do You Really Need?
The moment arrives. You’re writing your methodology chapter, and then you hit it—the sample size section. Your supervisor’s voice echoes in your head: “How did you determine your sample size? You need to justify this.”
Panic sets in. Do you use 100 respondents? 200? 384? Where do these numbers even come from?
You’re not alone. Sample size determination is one of the most confusing topics for Kenyan students. Yet it’s also one of the most common reasons supervisors send proposals back for revision. A weak or missing sample size justification can delay your approval by weeks.
Here’s the good news: determining your sample size doesn’t require a statistics degree. With a few formulas and some practical rules of thumb, you can confidently calculate—and defend—your sample size.
In this guide, we’ll cover the Yamane formula (the most popular among Kenyan students), the academic gold standard Krejcie & Morgan table, practical rules of thumb for different research designs, and how to write the sample size section that will impress your supervisor.
And if you get stuck along the way, Proposal Writers Kenya has experts ready to help you craft a methodology chapter that stands up to scrutiny.
What Is Sample Size and Why Does It Matter?
Sample size refers to the number of respondents or participants you will include in your study. Since you can rarely survey an entire population (imagine trying to interview every student at the University of Nairobi), you select a representative subset—your sample.
Why can’t you survey everyone?
Three reasons: time, cost, and accessibility. Surveying 10,000 people takes months and costs a fortune. Surveying 384 people takes weeks and costs significantly less. A well-chosen sample gives you results that are statistically similar to surveying everyone, but with a fraction of the effort.
What happens if your sample is too small?
Your results become unreliable. Patterns might appear that don’t actually exist, or real patterns might be missed. Your supervisor will rightly question whether your conclusions are valid.
What about a sample that’s too large?
While statistically fine, an unnecessarily large sample wastes your time, your respondents’ patience, and your budget. There’s no prize for surveying 2,000 people when 400 would have been sufficient.
Your supervisor wants to see that you’ve thought carefully about your sample size—not just picked a random number because it “felt right.”
Key Concepts You Need to Understand First
Before we dive into formulas, let’s clarify four essential concepts.
Population vs. Sample
Your target population is the entire group you want to study (e.g., all undergraduate students at Kenyatta University). Your sample is the subset you will actually survey (e.g., 350 students from that population). The key is ensuring your sample represents the population.
Confidence Level
This tells you how certain you can be that your sample reflects the population. The standard in social science research is 95% confidence. This means if you repeated your study 100 times, 95 of those studies would produce results within your margin of error.
Margin of Error (Confidence Interval)
This is the acceptable “wiggle room” in your results. The standard is ±5%. So if your study finds that 60% of students prefer online learning, with a ±5% margin of error, the true population value is likely between 55% and 65%.
Response Rate
Not everyone you invite will complete your questionnaire. Online surveys typically see 30-50% response rates. Paper surveys might reach 60-80%. If you need 384 completed responses but expect a 50% response rate, you need to invite approximately 768 people.
Method 1: The Yamane Formula (Most Popular for Kenyan Students)
The Yamane formula (developed by Yamane in 1967) is the most commonly used sample size formula in Kenyan undergraduate and master’s theses. It’s simple, widely accepted, and works perfectly for most research projects.
The Formula
n = N / (1 + N(e)²)
Where:
n = your required sample size
N = your total population size
e = your margin of error (usually 0.05 for 5%)
Worked Example 1: Population of 5,000 Students
Let’s say you’re studying students at a Kenyan university with a population of 5,000.
n = 5,000 / (1 + 5,000 × 0.05²)
First, calculate 0.05² = 0.0025
Then, 5,000 × 0.0025 = 12.5
Then, 1 + 12.5 = 13.5
Finally, 5,000 ÷ 13.5 = 370.37
Your sample size: 370 respondents (always round up)
Worked Example 2: Small Population of 800
If your population is smaller, your sample size decreases proportionally.
n = 800 / (1 + 800 × 0.0025) = 800 / 3 = 267 respondents
Worked Example 3: Large Population of 200,000
Here’s where the magic happens. For very large populations, sample size plateaus.
n = 200,000 / (1 + 200,000 × 0.0025) = 200,000 / 501 = 399 respondents
Notice that increasing the population from 5,000 to 200,000 only increased your sample from 370 to 399. This is why many studies use approximately 384-400 respondents regardless of population size once the population exceeds about 100,000.
Yamane Quick Reference Table
| Population Size | Sample Size (5% margin of error) |
|---|---|
| 100 | 80 |
| 200 | 133 |
| 500 | 222 |
| 1,000 | 286 |
| 2,000 | 333 |
| 5,000 | 370 |
| 10,000 | 385 |
| 50,000+ | 397 |
| 100,000+ | 400 |
Method 2: Krejcie & Morgan Table (Academic Gold Standard)
If your supervisor is particularly rigorous, they may ask you to use the Krejcie & Morgan table (1970). This is considered more precise than the Yamane formula and is often required for master’s and PhD theses.
How to Use the Table
Find your population size in the left column
Read across to find your required sample size
Example: A population of 2,500 requires a sample of 333 respondents (Krejcie & Morgan) compared to 345 using Yamane—very close.
How to Cite Krejcie & Morgan
Here’s the correct APA 7th citation you can use in your thesis:
“The sample size was determined using the Krejcie and Morgan (1970) table. With a target population of 2,500, a sample of 333 respondents was selected.”
Reference:
Krejcie, R. V., & Morgan, D. W. (1970). Determining sample size for research activities. Educational and Psychological Measurement, 30(3), 607-610.
Method 3: Rules of Thumb for Common Research Designs
Not all research uses formulas. Sometimes, you need practical rules of thumb.
Survey Research
Minimum: 100 respondents for descriptive surveys
Recommended: 200-400 for good statistical power
Correlational Studies (examining relationships between variables)
Minimum: 50 respondents
Recommended: 100+ respondents
Experimental Research
Minimum per group: 15-30 participants
Example: A study comparing three teaching methods needs 45-90 total participants
Qualitative Research (completely different rules)
Qualitative research prioritizes depth over breadth. Typical sample sizes:
Phenomenology: 5-25 interviews
Case study: 3-10 cases
Ethnography: 20-50 interviews
Thematic analysis: 10-12 interviews (Guest’s rule of thumb)
Step 4: Crafting Your Chapter Three (Research Methodology)
This chapter explains exactly how you will conduct your research. Be detailed—your supervisor needs to know your plan is feasible.
Research Approach and Design
Will you use quantitative, qualitative, or mixed methods? Justify your choice. Then specify your research design (e.g., descriptive survey, correlational design, case study).
Target Population and Sample
Define your target population clearly. Then explain your sample size and sampling technique. If using probability sampling, explain how you calculated sample size (Yamane formula is common). If using non-probability sampling, justify why.
Research Instruments
Describe how you will collect data. Will you use questionnaires, interview guides, observation checklists? Include examples of how you will measure each variable.
Validity and Reliability
Explain how you will ensure your instruments are valid (measure what they’re supposed to measure) and reliable (produce consistent results). Mention pilot testing.
Data Collection Procedures
Provide a step-by-step account of how data will be collected. Include how you will obtain consent and handle logistics.
Data Analysis
Specify how you will analyze data. For quantitative studies, name the statistical tests (e.g., descriptive statistics, correlation, regression). For qualitative studies, describe your thematic analysis approach.
Ethical Considerations
Address informed consent, confidentiality, anonymity, and the NACOSTI research permit requirements in Kenya.
How to Adjust Your Sample Size for Response Rate
This is the step most students forget—and supervisors always catch.
If you need 384 completed questionnaires but expect only 50% of invited respondents to participate, you must invite double.
The formula:
Final invitations = Desired sample ÷ Expected response rate
Example:
384 ÷ 0.50 = 768 invitations needed
For Kenyan students, realistic response rates are:
Online questionnaires (Google Forms, email): 30-40%
Paper questionnaires distributed in class: 60-80%
WhatsApp or social media distribution: 20-30%
Always inflate your target to account for non-response.
How to Write the Sample Size Section in Your Methodology Chapter
Here’s a complete template you can adapt for your thesis:
Sample Size Determination
The target population for this study consisted of [number] [describe population, e.g., third-year undergraduate students at the University of Nairobi]. Using the Yamane formula (1967) at a 95% confidence level and ±5% margin of error, the required sample size was calculated as follows:
n = N / (1 + N(e)²)
n = [population] / (1 + [population] × 0.05²)
n = [calculated sample size]To account for an anticipated [percentage]% non-response rate, the sample size was adjusted upward to [final number] respondents. A stratified random sampling technique was then employed to select participants from each stratum proportionally.
Common Mistakes Kenyan Students Make
| Mistake | Why It’s a Problem |
|---|---|
| No justification at all | Your supervisor will reject this immediately |
| Picking a random number like 100 | Looks arbitrary and unprofessional |
| Using Yamane when supervisor wants Krejcie & Morgan | Know your department’s preferences |
| Forgetting response rate adjustment | You’ll end up with fewer respondents than needed |
| Using a huge sample unnecessarily | Wastes time and resources |
Frequently Asked Questions
Can I use 30 respondents? Only for pilot studies or very specific experimental designs. For a main study, 30 is almost always too small.
Do I need sample size justification for qualitative research? Yes, but differently. Justify based on saturation rather than formulas.
What if my population is unknown? Use rules of thumb (e.g., 384 for surveys) and justify based on similar studies in your field.
Can I change my sample size after proposal approval? Usually yes, with supervisor approval and justification.
Conclusion
Determining your sample size doesn’t have to be terrifying. Whether you use the Yamane formula (n = N / (1 + N(e)²)), the Krejcie & Morgan table, or practical rules of thumb, the key is providing a clear, logical justification that your supervisor can follow.
Remember these three golden rules:
Calculate your sample size using a recognized formula or table
Adjust upward for expected non-response
Write your justification clearly in your methodology chapter
A well-justified sample size shows your supervisor that you understand research methodology and have planned your study properly. It’s one less reason for them to send your proposal back for revisions.
Still unsure about your sample size? At Proposal Writers Kenya, our methodology experts can help you calculate the perfect sample size for your study and write a justification that will impress any supervisor. We’ve helped hundreds of Kenyan students get their proposals approved—and we can help you too. Contact us today for a free consultation.